Related papers: On the Properties of Phononic Eigenvalue Problems
Given the $n\times n$ matrix polynomial $P(x)=\sum_{i=0}^kP_i x^i$, we consider the associated polynomial eigenvalue problem. This problem, viewed in terms of computing the roots of the scalar polynomial $\det P(x)$, is treated in…
We consider the problem of embedding eigenvalues into the essential spectrum of periodic Jacobi operators, using an oscillating, decreasing potential. To do this we employ a geometric method, previously used to embed eigenvalues into the…
We develop a method to determine the eigenvalues and eigenfunctions of two-boson Hamiltonians include a wide class of quantum optical models. The quantum Hamiltonians have been transformed in the form of the one variable differential…
We study an eigenvalue problem for functions in R^N and we find sufficient conditions for the existence of the fundamental eigenvalue. This result can be applied to the study of the orbital stability of the standing waves of the nonlinear…
In this article, we introduce a general theoretical framework to analyze non-consistent approximations of the discrete eigenmodes of a self-adjoint operator. We focus in particular on the discrete eigenvalues laying in spectral gaps. We…
We study eigenfrequencies and propagator expansions for damped wave equations on compact manifolds. Under the assumption of geometric control, the propagator is shown to admit an expansion in terms of finitely many eigenmodes near the real…
Semi-analytical methods for the modeling of guided waves in structures of constant cross-section lead to frequency-dependent polynomial eigenvalue problems for the wavenumbers and mode shapes. Solving these eigenvalue problems for a range…
We give a general method to calculate photonic band structure in the form of wave number $k$ as a function of frequency $\omega$, which is required whenever we want to calculate signal intensity related with photonic band structure. This…
This paper is dedicated to finding the quadrature operator eigenstates and wavefunctions of the most general $f$-deformed oscillators. A definition for quadrature operator for deformed algebra is derived to obtain the quadrature operator…
In this article, the existence of the spectrum (the eigenvalues) for the nonlinear continuous operators acting in the Banach spaces is investigated. For the study, this question is used a different approach that allows the studying of all…
Nonlinear eigenvalue problems with eigenvector nonlinearities (NEPv) are algebraic eigenvalue problems whose matrix depends on the eigenvector. Applications range from computational quantum mechanics to machine learning. Due to its…
This article can be considered as the first version of a book which the author plans to write about half-range problems in operator theory. It consists of two parts. The first part is based on lectures which the author delivered at…
We explore the block nature of the matrix representation of multiplex networks, introducing a new formalism to deal with its spectral properties as a function of the inter-layer coupling parameter. This approach allows us to derive…
For odd anharmonic oscillators, it is well known that complex scaling can be used to determine resonance energy eigenvalues and the corresponding eigenvectors in complex rotated space. We briefly review and discuss various methods for the…
We study the eigenvalues and the eigenvectors of $N\times N$ structured random matrices of the form $H = W\tilde{H}W+D$ with diagonal matrices $D$ and $W$ and $\tilde{H}$ from the Gaussian Unitary Ensemble. Using the supersymmetry technique…
The eigenvector-eigenvalue identities are expanded to include general mixing parameters. Some simple relations are obtained and they reveal an intricate texture of connections between the eigenvalues and the mixing parameters. Permutation…
Solving polynomial eigenvalue problems with eigenvector nonlinearities (PEPv) is an interesting computational challenge, outside the reach of the well-developed methods for nonlinear eigenvalue problems. We present a natural generalization…
Resonance frequencies are complex eigenvalues at which the homogeneous transmission problems have non-trivial solutions. These frequencies are of interest because they affect the behavior of the solutions even when the frequency is real.…
Operator eigenvalue problems play a critical role in various scientific fields and engineering applications, yet numerical methods are hindered by the curse of dimensionality. Recent deep learning methods provide an efficient approach to…
Confined optical phonons are discussed for a semiconductor nanowire of the Ge (Si)prototype on the basis of a theory developed some years ago. In the present work this theory is adapted to a non polar material and generalized to the case…